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CO2 Injection in Geological Formations: Determining Macroscale Coefficients from Pore Scale Processes

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Abstract

Carbon dioxide (CO2) injections in geological formations are usually performed for enhanced hydrocarbon recovery in oil and gas reservoirs and storage and sequestration in saline aquifers. Once CO2 is injected into the formation, it propagates in the porous rock by dispersion and convection. Chemical reactions between brine ions and CO2 molecules and consequent reactions with mineral grains are also important processes. The dynamics of CO2 molecules in random porous media are modeled with a set of differential equations corresponding to pore scale and continuum macroscale. On the pore scale, convective–dispersive equation is solved considering reactions on the inner boundaries in a unit cell. A unit cell is the smallest portion of a porous media that can reproduce the porous media by repetition. Inner boundaries in a unit cell are the surfaces of the mineral grains. Dispersion process at the pore scale is transformed into continuum macroscale by adopting periodic boundary conditions for contiguous unit cells and applying Taylor-Aris dispersion theory known as macrotransport theory. Using this theory, the discrete porous system changes into a continuum system within which the propagation and interaction of CO2 molecules with fluid and solid matrix of the porous media are characterized by three position-independent macroscopic coefficients: the mean velocity vector \({\bar{{\bf U}}^{\ast}}\) , dispersivity dyadic \({\bar{{\bf D}}^{\ast}}\) , and mean volumetric CO2 depletion coefficient \({\bar{K}^{\ast}}\) .

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Abbreviations

A :

A-function (cf. Eq. 19)

B :

B-field (cf. Eq. 23)

C:

Concentration, mol m-3

D :

Dispersivity dyadic, m2 s-1

D :

Molecular diffusion coefficient, m2 s-1

D g :

Diameter of a mineral grain, m

\({\bar{D}_{\rm x}}\) :

Macrotransport dispersivity coefficient in x-direction, m2s-1

\({\bar{{\bf D}}^{\ast}}\) :

Macrotransport dispersivity dyadic coefficient, m2 s-1

\({{\bf J}_{0}^\infty}\) :

Asymptotic probability flux density, m-2 s-1

K :

Permeability tensor, m2

\({\bar{K}^{\ast}}\) :

Macroscale depletion rate, or mean volumetric CO2 sequestration coefficient, s-1

\({\bar{K}_{\rm x}}\) :

Macrotransport depletion rate coefficient in x-direction, s-1

l :

Basic lattice vectors, m

l :

Unit cell length, m

L:

Length of porous bed, m

p :

Pressure, kPa

\({P_0^\infty}\) :

Steady state conditional probability density, fraction

r :

Radial vector, m

\({\bar{{\bf R}}}\) :

Macroscale position vector, m

R n :

Discrete position vector specifying the location of the nth unit cell, m

s :

Ratio of reactive surface to the interstitial space volume, m-1 (m2 m-3)

sg :

Total surface of the mineral grains in a unit cell, m2

U :

Superficial velocity of the fluid, ms-1

U :

Velocity vector in pore space around mineral grain(s), ms-1

\({\bar{{\bf U}}^{\ast}}\) :

Macrotransport velocity coefficient, ms-1

\({\bar{U}_{\rm x}}\) :

Macrotransport velocity coefficient in x-direction, ms-1

α :

Drag coefficient, dimensionless

\({\eta_{\rm CO_{2}}}\) :

CO2 storage/sequestration efficiency, fraction

κ :

Microscopic adsorption or reactivity coefficient, ms-1 (m3 m-2 s-1)

μ :

Fluid viscosity, pa s

ρ :

Density, kg m-3

σ :

Standard deviation, s

\({\phi}\) :

Porosity, fraction

\({\forall _0}\) :

Superficial volume of a unit cell, m3

\({\forall _g}\) :

Volume of mineral grains in a unit cell, m3

\({\forall_{\rm if}}\) :

Interstitial volume in a unit cell, m3

\({\forall _\infty}\) :

Total volume of the bed, m3

\({\partial \forall _0}\) :

Control surface of a unit cell, m2

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  1. F. Javadpour

    Present address: Jackson School of Geosciences, Bureau of Economic Geology, The University of Texas at Austin, Austin, TX, USA

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  1. Alberta Research Council, Calgary, AB, Canada

    F. Javadpour

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Javadpour, F. CO2 Injection in Geological Formations: Determining Macroscale Coefficients from Pore Scale Processes. Transp Porous Med 79, 87–105 (2009). https://doi.org/10.1007/s11242-008-9289-6

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  • DOI: https://doi.org/10.1007/s11242-008-9289-6

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